1. Field of the Invention
The invention relates to an adaptive filter and related methods for determining a filtering coefficient, and more particularly, to an adaptive filter operating based on an GSPT LMS Algorithm for adaptively determining the filtering coefficient so as to reduce complexity of the circuit arrangement of the adaptive filter.
2. Description of the Prior Art
With the advent of modern communication standards and the progress of VLSI technology, wireless communication services such as mobile person-to-person communication and indoor wireless network are becoming more and more popular and growing rapidly. Furthermore, wireless communication nowadays is not only confined to lower data rate transmission as the voice service but has also advanced to higher data rate transmission such as the multimedia service. However, with the increase of transmission rate and the enhancement of modulation technique, Inter-symbol interference (ISI) caused by the multi-path fading channel becomes more and more serious. Multi-path fading is a phenomenon in which radio waves are deflected and reflected due to the temperature gradients in the air, the surface of the earth, and the obstacles in the transmission path. The fading phenomenon results in several replicas of the transmitted signal appearing at the receiver end, and those replicas usually arrive at different times because the distance of each path is different. If those replicas span a period that is comparable to or even longer than a symbol period, the receiver might fail to correctly identify the transmitted signals. Therefore, it is necessary to install an adaptive filter in the wireless communication system to erase the interference effect so as to ensure the transmission quality.
Nowadays, the adaptive filter is widely used in various ways. Regarding wireless communication applications, for instance, the adaptive filter is used as the adaptive equalizer in the receiver of the wireless communication system. In U.S. Pat. No. 5,511,068, Sato et al. teach a mobile communication system with installed adaptive equalizers capable of transmitting and receiving a radio signal obtained by TDMA and CDMA without interference. Additionally, Wong et al. disclose an adaptive antenna array in the base station of the wireless network according to the concept of the adaptive filter in U.S. Pat. No. 6,330,460, “Simultaneous forward link beam forming and learning method for mobile high rate data traffic”. Besides being applied to the wireless communication system, the adaptive filter can be used in an active noise control for speakers.
As previously mentioned, the adaptive filter is widely used in the present wireless communication systems and noise-control modules. Considering the operating principles of the adaptive filter, one of the most acknowledged and popular adaptive algorithms is Least Mean Square(LMS) algorithm. Regarding the operating efficiency and performance, LMS algorithm has lower convergence speed comparing to other adaptive algorithms, that is, the adaptive filter based on LMS algorithm may erase ISI more slowly. On the other hand, the simple structure of LMS algorithm is suitable for hardware accomplishment and circuit arrangement. However, considering the trend of state-of-the-art VLSI circuit designing, due to that the users desire compact and low-power electronic devices, even LMS algorithm are too complicated for the circuit designers to implement because LMS algorithm requires multiplication. Therefore, the simplification of the operations of the adaptive filter becomes one of the most important issues in the industrial and academic circles.
In the general finite impulse response filter (FIR filter), multipliers are inevitable due to that general algorithms require multiplications. For significantly reducing the filter complexity, a well-known approach is to express the filter coefficient as sum of signed power-of-two (SPT). According to SPT method, the multiplication with SPT number can be achieved by only several shifters and adders, and the filter with SPT number is so-called 2PFIR filter(Powers-of-Two FIR filter or multiplierless FIR Filter). The above-mentioned concepts and methods related to complexity reduction of the filter algorithms are described in many journal papers or letters. For instance, Y. C. Lim et al. express the filter coefficient as sum of signed power-of-two in IEEE Transaction on Circuits and Systems II: Analog and Digital Signal Processing, Vol. 46, Issue 5, pp. 577-584, 1999. The resulting filter requires no general-purpose multiplier for multiplications and thus saves the chip area. R. M. Hewlitt et al. express the filtering coefficient with a Canonical Signed digit (CSD) system and apply the CSD system in the digital FIR filter system in IEEE Workshop on Signal Processing Systems, Vol. 8, pp. 414-426, 2000. In addition, Y. M. Hasan et al. further details other applications of CSD system in IEEE Signal Processing Letters, pp. 167-16, 2001.
As for applying both of SPT method and LMS algorithm to the adaptive filter, we can find related information in many documents and patents. C. L. Chen et al. disclose the way to adaptively adjust the filtering coefficient of the adaptive filter by SPT method and LMS algorithm in Proceedings of IEEE ISCAS-96, pp. 364-367, 1996. In U.S. Pat. No. 6,337,878, “Adaptive equalizer with decision directed constant modulus algorithm”, Endres et al. utilize a Constant Modulus Algorithm (CMA) to adaptively adjust the filtering coefficient of the adaptive equalizer combined with SPT method. CMA representation, which can be treated as an advanced LMS algorithm, pre-estimates the error value by a pre-determined table that takes various conditions into consideration for accurately estimating the error value and for raising the convergence speed. Moreover, in U.S. Pat. No. 6,418,164, “Adaptive equalizer with enhanced error quantization”, Endres et al. improve the above-mentioned CMA representation and enhance the pre-determined table for adaptively adjusting the filtering coefficient of the adaptive equalizer in the receiver end.
Generally speaking, the quality of the adaptive filter can rely on both the convergence speed and the residual error. Although the above-mentioned prior arts have contributed to the simplification of the operations of the adaptive filter, we find that the prior art still leaves lots of space for improvement regarding sufficiently reducing the system complexity. Moreover, most of the prior art cannot take care of both the convergence speed and the residual error while reducing the system complexity. Since the requirement of performance in a communication system may alter according to different situations, each of the above-mentioned prior art that only aims at certain improvement cannot cover the actual demands in a wireless communication system.